Two-coupled structural modulations in charge-density-wave state of SrPt₂As₂ superconductor

Transmission electron microscopy (TEM) study of SrPt₂As₂ reveals two incommensurate modulations appearing in the charge-density-wave (CDW) state below T_CDW ≈ 470 K. These two structural modulations can be well explained in terms of condensations of two-coupled phonon modes with wave vectors of q₁= 0.62a^* on the a^*-b^* plane and q₂= 0.23a^* on the a^*-c^* plane. The atomic displacements occur along the b-axis direction for q₁ and along the c-axis direction for q₂, respectively. Moreover, the correlation between q₁ and q₂ can be generally written as q₁= (q₂+a^*)/2 in the CDW state, suggesting the presence of essential coupling between q₁ and q₂. A small fraction of Ir doping on the Pt site in Sr(Pt_1-xIr_x)₂As₂ (x ≤ 0.06) could moderately change these CDW modulations and also affect their superconductivities.